Posted: October 1st, 2022

Business Decision Analytics under Uncertainty

Business Decision Analytics under Uncertainty – Fall 2022
Project 1
Please present your whole work with temporary, however sufficiently detailed rationalization. You possibly can discuss with the lectures
to help your dialogue. You should utilize a graphing calculator or pc software program to visualise the Question Assignment
when relevant. Submit your work on Canvas as a single Phrase doc; handwritten solutions usually are not
accepted. To Help grading and including feedback, don’t convert your work right into a pdf file[s].
Question Assignment 1 (40 factors)
You help your consumer to pick a location x = (x1 , x2) for a service facility that may serve Ok = 50 prospects
by offering a single (equivalent) commodity to every buyer. The power could be positioned wherever inside
the unit sq. zero  x1  1, zero  x2  1 (which may mannequin e.g., a 10 km by 10 km rectangular area scaled to
the unit sq.). The shoppers are modeled as factors pk = (pk1 , pk2) for ok = 1, … , Ok positioned inside the
unit sq.. Every buyer’s yearly demand is assumed to be a identified worth, and we assume that each one
calls for are glad. Nevertheless, prospects are assumed to be of various relative “weight”, proportionate
to the dimensions of their yearly demand for the commodity. This side is expressed by assigning weights wk for
ok = 1, … , Ok to the purchasers. For instance the issue, please see the determine under that reveals the unit
sq. (blue), a attainable (however not optimized) location for the power (black dot), and the places of the
“weighted” prospects (crimson dots of radius wk for ok = 1, … , Ok).
Assume that the space between the power location x and buyer pk is expressed by the so-called
Manhattan (l1-norm) distance perform
d(x, pk) = |x1 – pk1| + | x2 – pk2|.
Formulate a choice mannequin that optimizes the situation of the power. The standard of a location is expressed
by the weighted sum of the Manhattan distances between the power and the purchasers.
See web page 2 for Questions 2 to four.
Question Assignment 2 (20 factors)
Decide the convexity / nonconvexity properties of your facility location drawback. Primarily based on the
dialogue offered within the lectures, state whether or not this facility location drawback is anticipated to be “straightforward” or
“arduous” to unravel.
Question Assignment three (20 factors)
Assume now that the areas |x1 – x2| > zero.three, x1 + x2 > 1.5, x1
2 – x2 + zero.four < zero, and x1
2 + three x2
2 < zero.5 should be
excluded from consideration for the attainable location of the power. In comparison with the reply to 1.2, state
whether or not this facility location drawback is anticipated to be “simpler” or “tougher” to unravel.
Question Assignment four (20 factors)
Recommend an preliminary resolution that’s more likely to be a “good guess” of the answer to this facility location drawback.
Briefly clarify your alternative.

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